Question

A man standing in front of a vertical cliff fires a gun and hears the echo after 4 seconds. He moves 150 m towards the cliff and again fires the gun. This time he hears the echo after 3.6 seconds. Find the distance of the cliff from his first position.( Assume velocity of sound is not known.)

• A. 7500 m
• B. 750 m
• C. 550 m
• D. 5500 m

Answer 1

The correct option is B

750 m

Let the distance of cliff be d meters.

Since echo is reflection of the original sound, it will travel distance equal to twice the distance between man and cliff i.e. 2d.

Let the velocity of sound be v m/s

As we know, speed = distance/ time ,

Then for the first case

v = 2d/t1 = 2d/4 m/s ...........(i)

Now, after travelling 150 m towards the cliff,

Distance travelled by sound = 2(d-150) = (2d-300) m

Then, v = (2d-300)/t2 = (2d-300)/3.6 m/s ................(ii)

Equating the value of v from equations (i) and (ii), we get

(2d-300)/3.6 = 2d/4

Solving above equation, d = 750 m